Quantum Dots in Strong Magnetic Fields: Stability Criteria for the Maximum Density Droplet

TL;DR

This paper analyzes the stability of the maximum density droplet in quantum dots under strong magnetic fields, deriving exact criteria for its stability considering electron interactions and edge excitations.

Contribution

It provides the first exact stability criteria for maximum density droplets in quantum dots in strong magnetic fields, accounting for electron-electron interactions.

Findings

Derived exact stability conditions against edge excitations.

Established criteria for droplet stability with interior holes.

Highlighted simplifications due to broken time-reversal symmetry.

Abstract

In this article we discuss the ground state of a parabolically confined quantum dots in the limit of very strong magnetic fields where the electron system is completely spin-polarized and all electrons are in the lowest Landau level. Without electron-electron interactions the ground state is a single Slater determinant corresponding to a droplet centered on the minimum of the confinement potential and occupying the minimum area allowed by the Pauli exclusion principle. Electron-electron interactions favor droplets of larger area. We derive exact criteria for the stability of the maximum density droplet against edge excitations and against the introduction of holes in the interior of the droplet. The possibility of obtaining exact results in the strong magnetic field is related to important simplifications associated with broken time-reversal symmetry in a strong magnetic field.